Solve systems of equations by substitution for x-2y= -8 and 6x+7y=9

(-2,3)

Step-by-step explanation:

In order to solve the system using substitution, one of the variables must be defined so we can substitute it into the other equation.

We can easily define x in the second first by adding 2y from both sides

x - 2y = - 8

* add 2y to both sides *

x = 2y - 8

Now that we have defined x in the first equation we can plug in the defined value of x into the second equation

6x + 7y = 9

substitute 2y - 8 for x

6 (2y - 8) + 7y = 9

distribute 6 to -2y and -8

6 * 2y = 12y

6 * -8 = -48

12y - 48 + 7y = 9

combine like terms ( 12y + 7y = 19y )

19y - 48 = 9

add 48 to both sides

19y = 57

divide both sides by 19

19y/19 = y and 57/19 = 3

we're left with y = 3

Now that we have found the value of one of the variables we can plug it in to one of the equations ( note that plugging the value of y and solving for x in either equation will lead us to the same answer ) and solve for the other variable (x)

x - 2y = -8

y = 3

x - 2(3) = -8

multiply -2 and 3

x - 6 = -8

add 6 to both sides

x = -2

so x = -2 and y= 3

Therefore the solution to the system of equations is (-2,3)

a² + b²= c²

24² + 7² = c²

c= 25

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be